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A mathematical model for value estimation with public information and herding
1. | Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino |
References:
[1] |
G. Ajmone Marsan, N. Bellomo and M. Egidi, Towards a mathematical theory of complex socio-economic systems by functional subsystems representation, Kin. Rel. Mod., 1 (2008), 249-278.
doi: 10.3934/krm.2008.1.249. |
[2] |
P. Ball, Why Society is a Complex Matter, Springer-Verlag, Berlin Heidelberg, 2012.
doi: 10.1007/978-3-642-29000-8. |
[3] |
J. Berg, M. Marsili, A. Rustichini and R. Zecchina, Statistical mechanics of asset markets with private information, J. Quant. Finance, 1 (2001), 203-211. |
[4] |
Y. Biondi, P. Giannoccolo and S. Galam, Formation of share market prices under heterogeneous beliefs and common knowledge, Physica A, 391 (2012), 5532-5545.
doi: 10.1016/j.physa.2012.06.015. |
[5] |
A. Boccabella, R. Natalini and L. Pareschi, On a continuous mixed strategy model for evolutionary game-theory, Kinet. Relat. Models, 4 (2011), 187-213.
doi: 10.3934/krm.2011.4.187. |
[6] |
D. Borra and T. Lorenzi, Asymptotic analysis of continuous opinion dynamics models under bounded confidence, Commun. Pure Appl. Anal., 12 (2013), 1487-1499.
doi: 10.3934/cpaa.2013.12.1487. |
[7] |
J.-P. Bouchaud, Economics need a scientific revolution, Nature, 455 (2008), 1181.
doi: 10.1038/4551181a. |
[8] |
J.-P. Bouchaud, The (unfortunate) complexity of the economy, Physics World, 82 (2009), 28-32. |
[9] |
L. Boudin and F. Salvarani, Modeling Opinion Formation by Means of Kinetic Equations, in Mathematical modeling of collective behavior in socio-economic and life sciences, Birkhauser, Boston, 2010.
doi: 10.1007/978-0-8176-4946-3_10. |
[10] |
L. Boudin and F. Salvarani, The quasi-invariant limit for a kinetic model of sociological collective behavior, Kinet. Relat. Models, 2 (2009), 433-449.
doi: 10.3934/krm.2009.2.433. |
[11] |
S. Cordier, L. Pareschi and G. Toscani, On a kinetic model for a simple market economy, J. Stat. Phys., 120 (2005), 253-277.
doi: 10.1007/s10955-005-5456-0. |
[12] |
M. Cristelli, L. Pietronero and A. Zaccaria, Critical Overview of Agent-Based Models for Economics, Proceedings of the School of Physics E. Fermi, course CLXXVI, 2010. |
[13] |
B. During, P. A. Markowich, J. F. Pietschmann and M. T. Wolfram, Boltzmann and Fokker-Planck Equations modelling Opinion Formation in the Presence of strong Leaders, Proc. Royal Soc. A, 465 (2009), 3687-3708.
doi: 10.1098/rspa.2009.0239. |
[14] |
R. Gatignol, Théorie Cinétique des Gaz à Répartition Discréte des Vitèsses, (French) Lecture Notes in Physics, Vol. 36. Springer-Verlag, Berlin-New York, 1975. |
[15] |
E. Eyster and M. Rabin, naïve herding in rich-information settings, AEJ Microeconomics, 2 (2010), 221-243.
doi: 10.1257/mic.2.4.221. |
[16] |
T. Kaizoji and D. Sornette, Market Bubbles and Crashes, in Encyclopedia of quantitative finance, Wiley, New York, 2010.
doi: 10.1143/PTPS.162.165. |
[17] |
J.-M. Lasry and P.-L. Lions, Mean field games, Japan. J. Math., 2 (2007), 229-260.
doi: 10.1007/s11537-007-0657-8. |
[18] |
J. Lorenz, Continuous opinion dynamics under bounded confidence: A survey, International Journal of Modern Physics C, 18 (2007), 1819-1838.
doi: 10.1142/S0129183107011789. |
[19] |
T. Lux, Herd behaviour, bubbles and crashes, Economic Journal, 105 (1995), 881-896.
doi: 10.2307/2235156. |
[20] |
D. Maldarella and L. Pareschi, Kinetic models for socio-economic dynamics of speculative markets, Physica A, 391 (2012), 715-730.
doi: 10.1016/j.physa.2011.08.013. |
[21] |
M. Marsili, D. Challet and R. Zecchina, Exact solution of a modified El Farol's bar problem: Efficiency and the role of market impact, Physica A: Statistical Mechanics and its Applications, 280 (2000), 522-553.
doi: 10.1016/S0378-4371(99)00610-X. |
[22] |
Q. Michard and J.-P. Bouchaud, Theory of collective opinion shifts: From smooth trends to abrupt swings, Eur. Phys. J. B, 47 (2005), 151-159.
doi: 10.1140/epjb/e2005-00307-0. |
[23] |
B. Perthame, Trasport Equations in Biology, Frontiers in Mathematics. Birkäuser Verlag, Basel, 2007. |
[24] |
H. A. Simon, Invariants of human behavior, Annu. Rev. Psychol., 41 (1990), 1-19. |
[25] |
G. Toscani, C. Brugna and S. Demichelis, Kinetic models for the trading of goods, J. Stat. Phys., 151 (2013), 549-566.
doi: 10.1007/s10955-012-0653-0. |
show all references
References:
[1] |
G. Ajmone Marsan, N. Bellomo and M. Egidi, Towards a mathematical theory of complex socio-economic systems by functional subsystems representation, Kin. Rel. Mod., 1 (2008), 249-278.
doi: 10.3934/krm.2008.1.249. |
[2] |
P. Ball, Why Society is a Complex Matter, Springer-Verlag, Berlin Heidelberg, 2012.
doi: 10.1007/978-3-642-29000-8. |
[3] |
J. Berg, M. Marsili, A. Rustichini and R. Zecchina, Statistical mechanics of asset markets with private information, J. Quant. Finance, 1 (2001), 203-211. |
[4] |
Y. Biondi, P. Giannoccolo and S. Galam, Formation of share market prices under heterogeneous beliefs and common knowledge, Physica A, 391 (2012), 5532-5545.
doi: 10.1016/j.physa.2012.06.015. |
[5] |
A. Boccabella, R. Natalini and L. Pareschi, On a continuous mixed strategy model for evolutionary game-theory, Kinet. Relat. Models, 4 (2011), 187-213.
doi: 10.3934/krm.2011.4.187. |
[6] |
D. Borra and T. Lorenzi, Asymptotic analysis of continuous opinion dynamics models under bounded confidence, Commun. Pure Appl. Anal., 12 (2013), 1487-1499.
doi: 10.3934/cpaa.2013.12.1487. |
[7] |
J.-P. Bouchaud, Economics need a scientific revolution, Nature, 455 (2008), 1181.
doi: 10.1038/4551181a. |
[8] |
J.-P. Bouchaud, The (unfortunate) complexity of the economy, Physics World, 82 (2009), 28-32. |
[9] |
L. Boudin and F. Salvarani, Modeling Opinion Formation by Means of Kinetic Equations, in Mathematical modeling of collective behavior in socio-economic and life sciences, Birkhauser, Boston, 2010.
doi: 10.1007/978-0-8176-4946-3_10. |
[10] |
L. Boudin and F. Salvarani, The quasi-invariant limit for a kinetic model of sociological collective behavior, Kinet. Relat. Models, 2 (2009), 433-449.
doi: 10.3934/krm.2009.2.433. |
[11] |
S. Cordier, L. Pareschi and G. Toscani, On a kinetic model for a simple market economy, J. Stat. Phys., 120 (2005), 253-277.
doi: 10.1007/s10955-005-5456-0. |
[12] |
M. Cristelli, L. Pietronero and A. Zaccaria, Critical Overview of Agent-Based Models for Economics, Proceedings of the School of Physics E. Fermi, course CLXXVI, 2010. |
[13] |
B. During, P. A. Markowich, J. F. Pietschmann and M. T. Wolfram, Boltzmann and Fokker-Planck Equations modelling Opinion Formation in the Presence of strong Leaders, Proc. Royal Soc. A, 465 (2009), 3687-3708.
doi: 10.1098/rspa.2009.0239. |
[14] |
R. Gatignol, Théorie Cinétique des Gaz à Répartition Discréte des Vitèsses, (French) Lecture Notes in Physics, Vol. 36. Springer-Verlag, Berlin-New York, 1975. |
[15] |
E. Eyster and M. Rabin, naïve herding in rich-information settings, AEJ Microeconomics, 2 (2010), 221-243.
doi: 10.1257/mic.2.4.221. |
[16] |
T. Kaizoji and D. Sornette, Market Bubbles and Crashes, in Encyclopedia of quantitative finance, Wiley, New York, 2010.
doi: 10.1143/PTPS.162.165. |
[17] |
J.-M. Lasry and P.-L. Lions, Mean field games, Japan. J. Math., 2 (2007), 229-260.
doi: 10.1007/s11537-007-0657-8. |
[18] |
J. Lorenz, Continuous opinion dynamics under bounded confidence: A survey, International Journal of Modern Physics C, 18 (2007), 1819-1838.
doi: 10.1142/S0129183107011789. |
[19] |
T. Lux, Herd behaviour, bubbles and crashes, Economic Journal, 105 (1995), 881-896.
doi: 10.2307/2235156. |
[20] |
D. Maldarella and L. Pareschi, Kinetic models for socio-economic dynamics of speculative markets, Physica A, 391 (2012), 715-730.
doi: 10.1016/j.physa.2011.08.013. |
[21] |
M. Marsili, D. Challet and R. Zecchina, Exact solution of a modified El Farol's bar problem: Efficiency and the role of market impact, Physica A: Statistical Mechanics and its Applications, 280 (2000), 522-553.
doi: 10.1016/S0378-4371(99)00610-X. |
[22] |
Q. Michard and J.-P. Bouchaud, Theory of collective opinion shifts: From smooth trends to abrupt swings, Eur. Phys. J. B, 47 (2005), 151-159.
doi: 10.1140/epjb/e2005-00307-0. |
[23] |
B. Perthame, Trasport Equations in Biology, Frontiers in Mathematics. Birkäuser Verlag, Basel, 2007. |
[24] |
H. A. Simon, Invariants of human behavior, Annu. Rev. Psychol., 41 (1990), 1-19. |
[25] |
G. Toscani, C. Brugna and S. Demichelis, Kinetic models for the trading of goods, J. Stat. Phys., 151 (2013), 549-566.
doi: 10.1007/s10955-012-0653-0. |
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